OK, a few things:
1) A girl with a kid, 9 times out of 10, is NOT looking for a FWB relationship. If she is, then she's fvcked in the head and you need to get the hell out. The only way this is ok (this is rare) is if she only sees you infrequently, and the kid NEVER sees you. Otherwise, that kid will be even more fvcked up than he already is. I hope you're good enough not to do that to a kid. If you don't plan on being a father figure, don't even let the kid see you. Just to be clear, if she's just looking for fun with a male partner, I'm totally cool with that (as I'm sure you are). Just because she has a kid doesn't mean she can't have her fun, she just needs to think of the child first and keep him out of that life. She obviously should be safe (if it's just a sex thing, I hope she's requiring a condom), but that's just my opinion, and it only affects her if she should get anything that prevents her from being the parent she should be to her child (AIDS).
2) Assuming she's not looking for that type of relationship - while you obviously are - you need to be very clear with her about that very soon. It doesn't sound like you've said anything to her yet, so you need to. A friend of mine is a complete and utter man-whore and has all kinds of FWB relationships with girls: EVERY SINGLE ONE OF THEM wants more, and he's very clear with every single one of them that it will never happen. They continue to curse him in the morning, and come back that night for more. These are not stable women. The point is, my friend may be heartless, but in my mind he's completely free of guilt here. You have to be the same way. You need to be very up front with her that you're not looking for a serious relationship and you don't want to become a father figure for the child if you may not be in his life long enough.
3) So if it's not clear already, if she's not cool with the FWB thing, then just end it. Period. That's a situation you don't want to get into. You don't have to have sympathy for her, but at least have sympathy for the kid.